Dynamics of powerful radio galaxies

Analytical models describing the dynamics of lobed radio sources are essential for interpretation of the tens of millions of radio sources that will be observed by the Square Kilometre Array and pathfinder instruments. We propose that historical models can be grouped into two classes in which the forward expansion of the radio source is driven by either the jet momentum flux or lobe internal pressure. The most recent generation of analytical models combines these limiting cases for a more comprehensive description. We extend the mathematical formalism of historical models to describe source expansion in non-uniform environments, and directly compare different model classes with each other, and with hydrodynamic numerical simulations. We quantify differences in predicted observable characteristics for lobed radio sources due to the different model assumptions for their dynamics. We make our code for the historical models analysed in this review openly available to the community.